{"ID":2846173,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.02456","arxiv_id":"2511.02456","title":"On Convergence Rates of Spiked Eigenvalue Estimates: A General Study of Global and Local Laws in Sample Covariance Matrices","abstract":"This paper investigates global and local laws for sample covariance matrices with general growth rates of dimensions. The sample size $N$ and population dimension $M$ can have the same order in logarithm, which implies that their ratio $M/N$ can approach zero, a constant, or infinity. These theories are utilized to determine the convergence rate of spiked eigenvalue estimates.","short_abstract":"This paper investigates global and local laws for sample covariance matrices with general growth rates of dimensions. The sample size $N$ and population dimension $M$ can have the same order in logarithm, which implies that their ratio $M/N$ can approach zero, a constant, or infinity. These theories are utilized to det...","url_abs":"https://arxiv.org/abs/2511.02456","url_pdf":"https://arxiv.org/pdf/2511.02456v1","authors":"[\"Bing-Yi Jing\",\"Weiming Li\",\"Jiahui Xie\",\"Yangchun Zhang\",\"Wang Zhou\"]","published":"2025-11-04T10:34:24Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}